A uniform chain of length and total mass is pulled straight upward by a crane so that…
PHYSICS · Multi-part · CBSE · Physics · Laws of Motion · Laws of Motion
Problem
A uniform chain of length L and total mass M is pulled straight upward by a crane so that every point of the chain experiences the same constant upward acceleration a while the chain remains vertical and straight.
Take y to be the distance measured downward from the uppermost link (y=0 at the top, y=L at the bottom).
(a) Derive an expression for the tension T(y) at an arbitrary position y during the upward acceleration.
(b) Using your expression from part (a), determine the magnitude of the force that the crane must exert on the very top link of the chain.
(c) Suppose the crane motor can exert a maximum upward force equal to 1.80 times the weight of the chain. Calculate the greatest upward acceleration amax the crane can give the chain while keeping it taut and vertical.